Solve the following heat equation and write the solution as u(x, t) PDE: Ut = Uxx BCs: ux(0, t) = 0, ux(n,t) = 10 IC: u(x, 0): = 10x² 2π

Find the constant of proportionality. y is directly proportional to x. If x=30, then y=15.

Using r(t) = +²₁² + 3 cost₁ + 5 sint & at += π, find Nit), T(H), at, and aN

Write the given second order equation as its equivalent system of first order equations. " – 7.5u + 1.5u = -3 sin(3t), u(1) : = 0, u'(1) = 1.5 Use v to represent the "velocity function", i.e. v = u'(t). Use v and u for the two functions, rather than u(t) and v(t). (The latter confuses webwork. Functions like sin(t) are ok.) u 3= Now write the system using matrices: u d dt V and the initial value for the vector valued function is: u(1) v(1)